A remark on the Morse Theorem about infinitely many geodesics between two points

2011/05/19 by Erasmo Caponio, Caponio, Erasmo, Miguel Angel Javaloyes +1
Mathematics · #53C20 #53C22 #57B30 #58B20 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C20 #msc:53C22 #msc:57B30 #msc:58B20

paper · pdf · doi:10.48550/arxiv.1105.3923

Contribution to the proceedings of the "International Meeting on Differential Geometry, Córdoba 2010". 7 pages, AMSLaTex. v2: minor revision, one reference and related comments added

arxiv created 2011/12/28 · arxiv updated 2011/12/30

Abstract

We show that any two non-conjugate points on a forward or backward complete connected Finsler manifold can be joined by infinitely many geodesics which are not covered by finitely many closed ones, provided that the Betti numbers of the based loop space grow unbounded.

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